Delongmengis a Math Major in the Class of 2013. He Is Currently Pursuing a Ph.D. in Economics

Interview with DelongMeng

DelongMengis a math major in the class of 2013. He is currently pursuing a Ph.D. in Economics at Stanford.

Holden: You came to MIT planning on doing to math, but then decided to pursue economics. Could you tell us what led to the change?

Delong: I’ll just speak from a historical perspective. I met Gabriel Carroll in high school, and I asked him why are you doing economics? He said the problems he works on are similar to Olympiad combinatorics problems, so I became curious about economics.

My father would always say: do math or you’re not going to make money. He said economics is even easier and you’ll make more money, so why not do economics? When I came to MIT I saw some Chinese IPhO and IMO [International Physics/Math Olympiad] gold medalists, all doing economics, and I asked them, why are you doing economics? Their answer was basically the same as the one my father gave: if you do physics, you can’t find a job, so why not do economics?When I first came to MIT I thought this attitude was really bad. But that’s the Chinese way of doing things.

I was really confused, but at first I just started doing a lot of math. I thought since I did the IMO, and since I’m at MIT with all these resources, I can do well in math. Freshman year, I think I made some really bad mistakes in approaching math: I just itwas just like MOP [Math Olympiad Program] where people compete with others and solve problems. I didn’t even know what it meant to learn math. Since a lot of people took 18.701, I also took 18.701. But it turned out that a lot of people had learned linear algebra or group theory before, so taking 18.701 was good for them, but I didn’t have experience in any math beyond high school math. I found it very hard. Even then I still wanted to just study math: I thought that in high school I did math to get into college, but now I got into MIT, maybe I should just work hard. What really killed me was commutative algebra. I took it sophomore year, and thought it was a good class, but it turned out I actually didn’t understand it at all. After that class I took more math classes. I don’t think I actually understood them.

So I think my transition to economics is that I tried very hard to do math, but somehow it didn’t work the way I expected, and I felt I didn’t actually understand what I was taking. Sophomore summer, I did an economics UROP, and that was just like an Olympiad problem, so I thought, if I’m not doing very well in math, then I might just try economics.

But being a math major here helped me a lot with doing economics. For one thing, the undergrad research I didboiled down to a discrete math problem. I think the reason I could solve those problems is because coming from a math background, I wasn’t scared of solving those problems. I think that often when economic theorists see complicated math they try to avoid it, while for me I could spend an entire summer just thinking about one problem.That’s something that I got from doing math.

I did some undergrad math research with Stanley, and I also did Duluth. These research opportunities are really good. When I did more economics UROPs, I felt I wasn’t scared of doing research. I was used to getting stuck on problems.

The other thing is that before I came to MIT I was really scared of writing—both English and just writing in general. For my first UROP with Richard Stanley, it was a pain to write up my results. Writing a seven-page paper was very hard. But now, after Duluth, UROPs, and classes, after taking several of the humanities classes here, I’ve gotten better at writing. I can write a paper and not be scared.

The other thing I did here at MIT is running the HMMT with David Rush and Justin Brereton. I saw how things were on the other side of the competition. When I was a student, someone would give me problems and I would work on them. I could see now writing problems isn’t anything magical, justpeople coming up with good ideas. I learned to organize the event and handle the logistical issues, howto get something done.Organization is very hard actually. When I was organizing the HMMT, David Rush came up with good ideas about how to change the format of the competitions: he said you should never follow precedent. You should think about what makes sense.

After the HMMT I also did the UMA. I think doing the UMA helped me to coordinate events and organize things. I really liked the professor-student forum and the student research exposé in our year.

Holden:One thing that attracted you to economics was the math problems you found there. Was there anything else?

Delong: I can always say it’s more applied, but do I really care that it’s more applied? But it’s easier to explain to people why I’m doing what I’m doing. The economics I do is very mathematical, but there is a whole spectrum of things from very theoretical to very applied. I think it gave me the potential to in the future to think about big economics problems, such as how the government affects the economy.

Holden: What advice do you have for students coming to MIT who want to major in math but also might be interested in other areas, to decide what they want to do in the future?

Delong: I’m sure everyone says “do what you like, go explore,” and I think for me, the lesson is actually, go explore. When I came in I did not actually explore. I wanted to explore, but deep in my heart I was set on doing pure math. Also don’t rush yourself; that’s another lesson I learned. Freshman year, I thought if I didn’t take 18.701 I’d be behind. But actually, in my junior year I took a lot of GIRs, and that’s a waste of time for a junior.Freshman year, take all the basic classes and start exploring different things. I think that would be better.

Holden:You’ve stayed involved with the high school math community,for example, through competition math. What do you gain from the experience?

Delong: For me, personally, I just thought that MOP is this magical place where people have to be really smart to get in, and once you get in, you get into college and you’re the best person in your field. In college I found out that’s not entirely true.

This is something I felt recently when I went to MOP or when I was teaching in IdeaMath:The kids there are very smart and talented, but I hope they can learn more than just problem-solving and win competitions, and they can get more perspective about what doing math is like. Teaching is fun, grading is not as fun.

Holden:What do you think were your most memorable experiences here in the past four years, what did you learn? How do you think you’ve grown as a person?

Delong: In terms of academics, I’d say the most memorable experience was sophomore fall, taking commutative algebra.That term I think I had no idea what I was doing. I thought I was smart, taking this fancy class, but it wasn’t good for me. Academically, that’s one thing I learned: from now on to go one solid step at a time.

Grown as a person? I had some deep issues personally; I had a bad relationship with my parents, and had to come to terms with my identity in terms of being a Chinese immigrant, and having gone to school in the US.A lot of the time I tried to avoid those, but they still came back and confused me. One thing that helped me was that I was that in junior year, this guy in my church did a discipleship training with me, and we worked through some deep issues. I think having met more people outside the MOP community helped. Freshman year, I came in, I chose to be in Random Hall because I saw that’s where all the math majors lived. Pecker was the math floor.Over the past four years it changed a lot; now it’s not a math floor anymore. Just seeing that people exist outside math: that helped me understand that I can’t just know one group of people.

Holden: Could you tell us about the research you did?

Delong: With Richard Stanley it was an algebraic combinatorics problem, on reduced decompositions of the symmetric group. Several of his students had worked on the same thing.

For economics, my sophomore summer I did research on learning in repeated auctions. Basically, the idea is that you have this game.People have studied Nash equilibrium, but always argue about whether bidders will play Nash equilibrium. One way we can justify Nash equilibrium is to consider repeated bidding where people start off with some strategy and, as they see how their opponents behave, adjust their strategy. In the problem I studied, they respond to the distribution of their opponent’s history. I basically proved that in the system their strategies will converge to the Nash equilibrium. The problem sounds like an analysis problem but the gist of it is still very combinatorial. You boil the problem down to a sequence of matrices; once the first few columns converge, then the next column will converge.

The other problem I did was matching. In school districts in Boston, when people apply to public schools, they have to go through a centralized matching system where students will submit their preferences. The school board takes into account all these preferences and assigns you to a school. There are schools that are very popular, so you need some kind of mechanism to decide which students get into which schools. There’s this algorithm called the Top Trading Cycle algorithmwhich gives that. But in this algorithm, you need schools to rank students, and in reality, what the schools do is just run a randomized lottery for all the students. What I studied is how could schools run their lotteries? There are two ways to do it: one way is to have a centralized lottery where the school board says, here is a ranking of all the students, now all the schools will use that ranking. The other is for each school to generate its own lottery. Which one is better for the students? Intuitively you’d think that you want multiple lotteries, because if you get screwed at one school, you want a chance at another school, but actually if you look at the entire distribution, it’s not clear that one is better than the other. I proved an equivalence result under some assumptions on how students rank their schools.

Holden: What do you see yourself doing in the future?

Delong:If you asked me this question ten years ago, I would say, be a professor. I guess that’s always my default answer. I haven’t really thought about any alternatives. But I don’t know, in grad school, especially if I do economics things may change. There are a lot of jobs other than professors.

Holden:What other things do you like to do besides math and economics?

Delong: I like listening to Chinese songs, just to relax. I try to go to the gym. I also read the New York Times.

Holden: Do you have any other advice for MIT math majors?

Delong:Don’t copy psets.

Holden: Thank you, Delong.